Assembling Ordered Crystals with Disperse Building Blocks

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

As Published http://dx.doi.org/10.1021/acs.nanolett.9b02508

Publisher American Chemical Society (ACS)

Version Final published version

Citable link https://hdl.handle.net/1721.1/129495

Detailed Terms http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article published under a Creative Commons Non-Commercial No Derivative Works (CC-BY-NC-ND) Attribution License, which permits copying and redistribution of the article, and creation of adaptations, all for non-commercial purposes.

Letter

Cite This: Nano Lett. 2019, 19, 5774−5780 pubs.acs.org/NanoLett

Assembling Ordered Crystals with Disperse Building Blocks † † Peter J. Santos, Tung Chun Cheung, and Robert J. Macfarlane* Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States

*S Supporting Information

ABSTRACT: Conventional colloidal crystallization techniques typically require low dispersity building blocks in order to make ordered particle arrays, resulting in a practical challenge for studying or scaling these materials. Nano- particles covered in a polymer brush therefore may be predicted to be challenging building blocks in the formation of high-quality particle superlattices, as both the nanoparticle core and polymer brush are independent sources of dispersity in the system. However, when supramolecular bonding between complementary functional groups at the ends of the polymer chains are used to drive particle assembly, these “nanocomposite tectons” can make high quality superlattices with polymer dispersities as large as 1.44 and particle diameter relative standard deviations up to 23% without any significant change to superlattice crystallinity. Here we demonstrate and explain how the flexible and dynamic nature of the polymer chains that comprise the particle brush allows them to deform to accommodate the irregularities in building block size and shape that arise from the inherent dispersity of their constituent components. Incorporating “soft” components into nanomaterials design therefore offers a facile and robust method for maintaining good control over organization when the materials themselves are imperfect. KEYWORDS: Nanoparticles, self-assembly, dispersity, polymer brushes, supramolecular chemistry

olloidal crystallization is an eﬀective means of manipulat- synthetic polymers as surface ligands (Figure 1).16 Interest- C ing material structure at the nanometer length scale, as ingly, although NCTs have dispersity originating from both chemical interactions between nanoparticle building blocks can their nanoparticle core and their polymer brush, they can still be used to program their assembly into ordered lattices.1,2 A form lattices with long-range order. We hypothesize that the wide variety of surface ligands have been used to control these ability of NCTs to spontaneously form crystalline lattices interactions and thereby manipulate particle assembly, where despite their inherent size and shape inhomogeneity arises the most stable phases typically maximize either particle from the ability of the polymer brush to easily deform as a packing density or the number of favorable interactions means of maximizing favorable supramolecular interactions between particles’ surface ligands.3,4 In all of these strategies, between particles. Thus, the establishment of appropriate particle size and shape dispersity are regarded as a negative design and processing strategies could enable these “soft” building blocks to overcome signiﬁcant variations in either factor that must be overcome to create well-ordered crystals, as −

See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. 17 19 irregularity in building block shape results in inefficient packing particle core size or ligand length. Here we explain how − Downloaded via MASSACHUSETTS INST OF TECHNOLOGY on September 23, 2019 at 12:46:48 (UTC). and limitations to interparticle surface contacts.5 7 As a result, the concept of ligand softness affects the processing pathways many impressive strategies to minimize dispersity in the used to obtain NCT-based colloidal crystals, as well as how particle assembly process have been developed, including these highly deformable surface ligands can mask imperfections 20 multiple techniques for the synthesis of monodisperse particles in particle size or shape during assembly. Ultimately, this − of different shapes,8 10 the use of biopolymer cages to dictate strategy allows for highly disperse nanoparticle components the directionality of interparticle bond formation,11,12 or even (up to 23% variation in particle core diameter) to form the use of molecularly precise biomacromolecules with superlattice architectures without any reduction in crystal ∼ − controlled surface functionalization as colloidal building quality, well beyond the 2 10% limit that is typically − blocks.13 15 However, all of these methods have limits in the required for maximizing the quality of other colloidal crystals. composition of the particles that can be used and tend to result As a result, NCTs represent a unique building block for fi in a trade-off between the quality and quantity of the building nanomaterial synthesis that has signi cant potential for making blocks that can be made. scalable particle-based materials. In contrast to colloidal crystallization approaches that aim to use the least disperse building blocks possible, we have recently Received: June 20, 2019 reported a new self-assembling particle called the Nano- Revised: July 25, 2019 composite Tecton (NCT), which uses inherently nonuniform Published: July 26, 2019

bonding pair. When NCTs with complementary supramolecular binding groups are combined, multiple hydrogen bonds form between the particles; these bonding interactions have been demonstrated to drive the formation of body- centered cubic (bcc)-type superlattices when the NCTs are thermally annealed.16 NCTs are amenable to thermal annealing because the hydrogen bonding interactions are relatively weak, and heating to mild temperatures (below 80 °C) is therefore sufficient to enable rearrangement. Given the inherent dispersity in both the particle sizes and shapes (previous work has demonstrated crystals for particle sizes with a relative standard deviation (RSD) of 15% and polymers with Đ of ∼1.1), the ability of NCTs to adopt conformations with long-range order is somewhat surprising. Understanding and controlling how these soft, high dispersity polymer shells affect crystallization therefore requires first determining how crystal formation is affected by processing pathway, as well as any upper bound in crystal quality that may be imposed on these assembled lattices via the use of a nonuniform and deformable polymer ligand coating. Figure 1. Nanocomposite Tecton assembly scheme. (a) NCTs fi consist of a nanoparticle core, a polymer shell, and a supramolecular The simplest potential thermal annealing pro le to generate binding group. When complementary NCTs are combined, hydrogen ordered NCT arrays is to heat and hold the initially amorphous bonds form between them to drive assembly. (b) Particles containing aggregates at a temperature close to their melting temperature 21 a soft, polymeric shell are more tolerant of dispersity, and when (Tm), analogous to recrystallization and grain growth coupled with an enthalpic driving force they can crystallize into well- processes in classical atomic systems (Figure 2a).22 When organized structures. this thermal annealing profile is used, the NCTs are able to form an ordered lattice but small-angle X-ray scattering The NCTs used in this work consist of gold nanoparticle (SAXS) data indicate that this annealing profile results in (AuNP) cores coated with polystyrene brushes (Figure S1) highly polycrystalline samples with small grain sizes ∼250 nm that terminate in either diaminopyridine (DAP) or thymine in diameter. The small average size of these grains is not (Thy) motifs that constitute a complementary hydrogen entirely unexpected, as the dispersity of the polymer brush

ﬁ Figure 2. In situ SAXS measurements of NCT crystallization. (a) Temperature pro le of NCTs heated from room temperature to their Tm and held there while they crystallize (black trace). Annealing results in a gradual increase in domain size, as estimated by the Scherrer equation, but after a 30 min treatment the crystal quality is still poor (blue data points). (b) When NCTs are cooled from an elevated temperature, the nucleation and growth process results in larger crystalline domains. However, further quenching from Tm to room temperature causes the formation of additional amorphous phase aggregates from unassembled NCTs. (c) Cooling the NCTs from an elevated temperature at 4 °C/min results in highly ordered crystals at all temperatures.

5775 DOI: 10.1021/acs.nanolett.9b02508 Nano Lett. 2019, 19, 5774−5780 Nano Letters Letter

Figure 3. NCT assembly is not strongly affected by the dispersity of the polymer shell. (a) GPC traces showing the increasingly disperse batches of polymers used in NCT synthesis. All polymer batches have a number-average molecular weight of 12 kDa, polymer dispersity is controlled by blending together multiple low dispersity polymers of different molecular weights. (b) The melting temperature of the NCTs (bottom), indicative of the strength of NCT−NCT association, does not have a strong relationship with polymer dispersity. Additionally, there is no statistically significant difference in domain size, as estimated by the Scherrer equation (top) for NCTs assembled with polymers of varying dispersity. Error bars represent standard deviations, n = 3. (c) SAXS diffraction patterns of NCTs assembled with increasingly disperse polymers. The dashed line is a simulated SAXS diffraction pattern of a bcc crystal structure. heights and the flexibility of the polymer chains means that the whereas some small amounts of additional growth may occur number of DAP-Thy complexes that can form in a perfectly due to individual NCTs attaching to these precipitated ordered state and a kinetically trapped state should be similar. structures, grain growth rates are limited compared to the Because the driving force for assembling NCTs is the solution-suspended aggregates. Therefore, at temperatures formation of supramolecular complexes, the energy difference within the thermal window between the fully aggregated and between these two states with similar numbers of hydrogen fully melted state there exists an equilibrium between free bonds would be predicted to be relatively small, reducing the NCTs dispersed in solution and precipitated aggregates that thermodynamic force for forming large crystallites. are unlikely to either grow or reorganize, indicating that the To avoid the formation of the kinetic traps that limit crystal crystallite sizes observed in Figure 2c represent a practical grain size, an alternate annealing pathway would be to heat the maximum. This limitation in domain size was confirmed by NCTs until completely melted, then drop the solution to just controlling the rate of cooling during NCT crystallization. For ° below the Tm and hold the NCTs in this state until crystal cooling rates slower than 8 C/s, only a slight increase in formation is complete (Figure 2b). This thermal profile should crystal quality or domain size was observed as the cooling rate grow large, high quality crystals because quenching the sample was decreased (Figure S7). Nevertheless, the kinetic traps just below its melting temperature suppresses the number of caused by both the dispersity in NCT size and the soft nature nucleation events, resulting in a small number of initial of their bonding interactions can be minimized by using a crystallites that grow to form large grains. Indeed, this solution cooling rate to control the nucleation and growth rates formation pathway is commonly used to generate large atomic of crystals in solution within this fundamental limit. or molecular crystals.23 However, although the initial Given that NCT crystallization arises from the formation of aggregates that formed immediately below Tm were more multiple DAP and Thy hydrogen bonds, it therefore could be crystalline than the samples heated from room temperature, hypothesized that altering the dispersity of the polymer brush quenching from this high T (to 25 °C) resulted in a noticeable height could also affect crystallization by altering the ability of reduction in crystal quality (as indicated by the broader peaks DAP and Thy groups on adjacent particles to form in the SAXS pattern). This reduction in quality stems from the supramolecular complexes. Larger variations in polymer fact that NCTs exist in equilibrium between their assembled chain lengths across the surface of an NCT would be expected and melted state across a large thermal window; this broad to decrease crystallinity, as they would effectively alter the melting transition arises from the multivalent nature of the overall shape of each NCT, and therefore the thermodynamic bonding interactions between particles (Figure S5).24,25 driving forces for forming ordered arrays. To investigate the Therefore, to give the largest domains, the NCT solution effects of polymer dispersity on NCT crystallization, a series of must be brought into equilibrium at each temperature between DAP-terminated polymers ranging in molecular weight from the fully melted and fully aggregated states. Interestingly, when 10 to 16 kDa, each with Đ < 1.05, was synthesized by atom the NCTs are slowly cooled across this thermal window, the transfer radical polymerization (ATRP).26 Đ of the NCT resulting crystals exhibit a sharper SAXS diffraction pattern polymer brushes was varied by combining these batches of corresponding to larger grain sizes (∼400 nm) but these crystal low-dispersity polymers in different ratios to obtain polymer sizes reach a maximum early in the transition and only become blends where the average polymer length remained constant at more numerous instead of larger (Figure S7a). This upper limit ∼12 kDa, but the overall values of Đ varied between 1.05 and on domain size is likely due to the fact that crystallites of a 1.44 (a value that might be obtained from an uncontrolled free given mass can be observed to precipitate out of solution; radical polymerization).27 We would note that control

5776 DOI: 10.1021/acs.nanolett.9b02508 Nano Lett. 2019, 19, 5774−5780 Nano Letters Letter experiments were also performed to ensure that the polymer 10 and 16 kDa NCTs), meaning that monitoring the Tm of grafts on the NCTs possessed the same polymer length NCTs consisting of mixtures of these polymer lengths could distributions as the polymer stocks used to functionalize each potentially indicate which polymer length dictates the strength Đ batch of particles. In other words, the values of for the of inter-NCT bonding (Figure S6). Interestingly, doping a low polymer brushes on each NCT were identical to the values of Đ molecular weight polymer brush with longer chains has of the stock solutions (Figure S2). These samples were then ff ff annealed by slowly cooling them from high temperatures to di erent e ects on NCT thermodynamics than doping a obtain the most ordered lattice possible. high molecular weight brush with shorter polymer chains Surprisingly, no correlation between polymer dispersity and (Figure 4a). When shorter polymers are doped into the long- crystallinity was observed; all of the samples exhibited indistinguishable SAXS patterns, indicating that the final crystal structures were identical in quality. Even NCTs with a strongly bimodal distribution of polymer lengths showed no change in their average crystallite domain size, lattice parameter, or degree of long-range ordering (Figure 3b,c). Prior theoretical work28 has described polymer brushes containing chains with varying molecular weight and can provide an interpretation consistent with the experimental results presented here. Specifically, the preservation of crystallinity suggests the NCTs retain an isotropic config- uration, even when loaded with disperse polymer brushes. Prior models and experiments suggest that having high and low molecularweightpolymersadjacenttooneanotheris energetically favorable due to a positive entropy of mixing, and therefore no phase segregation or patches of different polymer lengths are expected to occur along the surface of the particle, although there may be differences in the brush − conformation.28 30 More simply, although individual polymer chains lengths can vary, the average brush height remains largely isotropic across the surface of the entire particle. Nevertheless, individual polymer chains may experience different entropic penalties when confined within an NCT− NCT bond. When adjacent NCTs form DAP-Thy hydrogen bonds, the polymer chains engaged in bonding experience a severe reduction in the number of accessible conformations, resulting in a large decrease in entropy. When an NCT brush consists of polymer chains of varying molecular weight, the magnitude of this change in entropy would be dependent on polymer length, as shorter polymer chains whose ends are not already near the surface of the NCT require additional conformation restriction in order to form hydrogen bonds (i.e., shorter chains need to stretch more to reach their NCT neighbors). It is therefore surprising that increasing the dispersity of the polymer brush does not affect the binding strength of the NCTs, as indicated by their relatively static Tm regardless of polymer dispersity (Figure 3b). However, the prior model Figure 4. Assembling NCTs with bimodal mixtures of long and short mentioned above suggests that a polymer brush can minimize polymer chains reveals the dynamics of the polymer brush. (a) Polymer chains that are significantly longer than the average brush its free energy by segregating the chain ends along the brush height are presented at the periphery of the NCT and are thus always height coordinate of the system as a function of polymer 28 able to participate in bonding (left). Conversely, polymer chains that molecular weight. In other words, it is energetically are significantly shorter than the average brush height are buried in unfavorable for the longer polymers to bury their chain ends the polymer brush and do not readily participate in interparticle in the interior of the brush, but instead they will on average bonding (right). (b) Increasing the fraction of long polymer chains in have their termini further from the surface of the particle than the bimodal distribution (mixtures of 10 and 16 kDa polymers) the shorter ones. As a result, interactions between the longest decreases the melting temperature of the NCTs. However, when the polymer chains on bound NCTs would dominate the fraction of a long polymer surpasses 40%, the melting temperature thermodynamics of NCT assembly, explaining the lack of plateaus at a value corresponding to the Tm of NCTs functionalized significant variation in either crystal quality or melting with just the long polymer. This trend suggests the assembly behavior is dominated by only the longer polymer chains. (c) Despite the lack temperature as a function of brush dispersity. of change in Tm above the 40% longer polymer, the interparticle To further verify this hypothesis, NCTs were coloaded with spacing consistently increases with the growing fraction of long a bimodal mixture of varying fractions of long and short polymer, signifying the presence of the shorter polymers are still polymer chains. NCTs made with the two different polymers contributing to the overall height of the brush by altering the free ff ∼ ° ff have a stark di erence in Tm,( 10 Cdi erence between the volume occupied by the longer polymer chains.

5777 DOI: 10.1021/acs.nanolett.9b02508 Nano Lett. 2019, 19, 5774−5780 Nano Letters Letter polymer NCTs (right-most data points, Figure 4b), the Tm NCTs may be able to tolerate greater deviations in particle size remains largely unchanged. This lack of change in Tm is or shape than these previous colloidal crystallization methods. consistent with the hypothesis that shorter chains dispersed To confirm this prediction, NCTs were synthesized with among an otherwise high molecular weight brush would be nanoparticle core diameters of 19, 24, and 28 nm, each with a forced to undergo significant stretching to reach the bonding particle diameter relative standard deviation (RSD) < 11.5%. plane between NCTs, and the corresponding entropy penalty The three different sizes were combined in ratios that associated with this stretching means that it is energetically maintained an average diameter of 24 nm but varied the unfavorable for them to strongly contribute to NCT assembly. overall distribution of inorganic particle core sizes up to ∼23% Thus, the Tm remains fairly constant with an increasing (representing a bimodal distribution of 19 and 28 nm spheres, amount of shorter polymers in a majority long-polymer brush. Figure S3). These samples were annealed by slow cooling Alternatively, when longer polymers are added to a low through their melting temperature and analyzed with SAXS. molecular weight brush, the melting temperature quickly drops Astonishingly, all samples with the exception of the 23% RSD (left-most data points, Figure 4b). The supramolecular binding system exhibited crystals of identical quality, and even the 23% groups on these longer chains are close to the exterior of the RSD sample exhibited only slight traces of a nonuniform NCT, and can readily participate in hydrogen bonding, crystal structure (evidenced by a slight shoulder in the SAXS regardless of the length of the nearby polymer chains. As a ∼ result, the height of the brush gradually increases with pattern at q 0.011) (Figure 5). There was also no observed increasing amounts of longer polymer, as is reflected in the shift in the average lattice parameter as a function of particle larger lattice parameter (Figure 4c). The shorter polymers are size dispersity, nor was there any evidence of observable phase forced to incur an entropic stretching penalty to participate in segregation of the smaller or larger particles within a crystal. If the larger and smaller particles phase segregated into separate bonding, resulting in a lowered Tm. As the necessary degree of stretching increases with a larger fraction of longer polymer, hydrogen bonds between the shorter polymers no longer improve the stability of the lattice. Above this point (∼40% long polymer for this system), these longer chains are able to dominate the assembly process, dictating the thermodynamics of NCT assembly (indicating the lack of substantial change in Tm between 40% and 100% long polymer). The observation that longer polymer chains can encapsulate the shorter ones in the brush are in agreement with prior experimental work.31 Therefore, dispersity in polymer molecular weight has a minimal effect on the overall dimensions of the NCT, as the brush can stretch and compress to account for local variations in polymer length. Although the softness of the polymer brush is observed to aid in NCT crystal formation despite any inherent inhomogeneity in polymer chain length, the nanoparticle core of NCTs is an additional source of dispersity in the NCT architecture, and unlike the polymer brush it is not capable of dynamically changing its shape. In colloidal crystals formed due to entropically driven close packing, small variations in particle size make the formation of ordered lattices impossible, even in the case of polymer grafted nanoparticles.32,33 In hard- sphere packing, it has been theoretically calculated and experimentally shown that the order−disorder transition is thermodynamically prohibited above a terminal dispersity between 6 and 11%.34,35 Prior work has demonstrated that adding bonding interactions that drive lattice formation via enthalpy maximization can enable more disperse building blocks to form ordered arrays. However, these systems still have limitations in the amount of dispersity that can be tolerated. For example, colloids coated with rigid dsDNA typically only form ordered arrays at particle dispersities of ∼10% or less, and only when the length of the DNA ligands is comparable to the radius of the particles being assembled.36 Other examples have also been demonstrated to create mesoscale structures from disperse mixtures of nanoparticles but these typically occur through fractionalization or self- Figure 5. SAXS patterns of NCT assemblies synthesized with varying nanoparticle core dispersities. Combinations of 19, 24, and 28 nm limiting processes that do not incorporate all particles present AuNPs were used to prepare sets of NCTs where each NCT batch in solution or do not control particle coordination environ- 37,38 had an average core diameter of 24 nm but RSDs ranged from 8.8% to ment. Given the above-demonstrated ability of the NCT 22.8% (inset numbers). After thermal processing, all sets of NCTs polymer brush to accommodate significant variations in were able to form bcc crystals with almost no discernible change to polymer brush height, it could also be hypothesized that crystal quality.

5778 DOI: 10.1021/acs.nanolett.9b02508 Nano Lett. 2019, 19, 5774−5780 Nano Letters Letter crystallites, this would be noted by a gradual broadening of the potentially amenable to the use of size- and shape-disperse SAXS peaks with increasing deviation in particle sizes, as well nanoparticle building blocks that may not form ordered − as a reduced number of observable higher order peaks due to crystals when using other assembly methods.33 35 NCTs are this broadening. In other words, the final state would consist of therefore a useful platform for understanding colloidal self- multiple different crystallites with varying lattice parameters assembly, and their easy processing and resistance to dispersity due to the differences in particle core diameters in each make them a valid candidate for the scalable synthesis of crystallite; this is clearly not observed in the SAXS patterns, ordered nanomaterials. which all exhibit nearly identical peak widths and number of higher order scattering peaks. Furthermore, the changes in the ■ ASSOCIATED CONTENT scattering patterns’ form factors at higher q (∼0.05−0.1) *S Supporting Information indicate that the dispersity of the particles within the lattices The Supporting Information is available free of charge on the correlates with the dispersity of the NCT stock solutions ACS Publications website at DOI: 10.1021/acs.nano- (Figure S4).39 Finally, the fact that all particles in each sample lett.9b02508. precipitated out of solution, combined with the observation − ff Materials and Methods; Scheme S1; Figures S1 S7; that there was no di erence in crystal quality or lattice Tables S1−S5 Supplementary References 1−5(PDF) parameter at different points within the precipitate also implies that the RSD in particle size within each lattice is comparable AUTHOR INFORMATION to the initial RSD of particle sizes in the stock solutions. In ■ short, the softness of the polymer ligands appears to Corresponding Author * completely mask variations in particle size or shape within E-mail: [email protected]. the regime studied, meaning that even at 23% RSD (mixtures ORCID of NCTs with 19 and 28 nm average core sizes), the soft Robert J. Macfarlane: 0000-0001-9449-2680 polymer brushes adjusted to allow all particles to form an Author Contributions † average crystal lattice parameter. The degree of deformation of P.J.S. and T.C.C. contributed equally. the polymer brush required to assemble such disperse Notes nanoparticles (∼5 nm) is comparable to the amount of The authors declare no competing financial interest. polymer stretching measured previously (Figure 4c), consistent with these prior results. It is hypothesized that shorter ■ ACKNOWLEDGMENTS polymers would be less capable of deforming and so would only tolerate smaller variations in nanoparticle core size. This work was primarily supported by an NSF CAREER The surprising ability of NCTs to crystallize even with Grant, award number CHE-1653289, and made use of the particle size deviations several times greater than is typically MRSEC Shared Experimental Facilities at MIT, supported by required by multiple other colloidal assembly methods can be the NSF under Award DMR 14-19807. P.J.S. acknowledges understood by examining how NCT design differs from these support by the NSF Graduate Research Fellowship Program more commonly studied nanoparticle superlattice building under Grant 1122374. SAXS experiments at beamline 12-ID-B blocks. Colloidal crystals that assemble through a drying- at the Advanced Photon Source at Argonne National mediated process require that each particle be as close to Laboratory were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under uniformity as possible, as these crystals do not have a deep fi energy minimum and thus variance in particle diameter can contract DE-AC02-06CH11357. This work bene ted from the significantly reduce the favorability of packing. This trend can use of the SasView application, originally developed under NSF award DMR-0520547. SasView contains code developed even be observed even when assembling polymer brush-coated ’ particles that are soft and capable of deforming to with funding from the European Union s Horizon 2020 accommodate deviations in particle size, as the lack of an research and innovation program under the SINE2020 project, enthalpic driving force means that alterations to packing Grant Agreement 654000. fi fraction (and thus entropy) can have a signi cant destabilizing REFERENCES effect on assembly. However, because NCTs are assembled via ■ supramolecular bonding, the enthalpic driving force for NCT (1) Pileni, M.-P. Self-Assembly of Inorganic Nanocrystals: crystallization is much stronger, offsetting some of the entropic Fabrication and Collective Intrinsic Properties. Acc. Chem. Res. ff 2007, 40 (8), 685−693. considerations that are a ected by particle dispersity. NCTs do (2) von Freymann, G.; Kitaev, V.; Lotsch, B. V.; Ozin, G. A. Bottom- get stuck in kinetic traps as a result of these enthalpic bonding ff up Assembly of Photonic Crystals. Chem. Soc. Rev. 2013, 42 (7), interactions, but proper thermal processing is e ective at 2528−2554. overcoming them. Dispersity is therefore hypothesized to (3) Bishop, K. J. M.; Wilmer, C. E.; Soh, S.; Grzybowski, B. A. mostly affect NCTs through geometric obstruction, where Nanoscale Forces and Their Uses in Self-Assembly. Small 2009, 5 differences in particle size cause such severe lattice strain that (14), 1600−1630. the formation of large crystalline domains becomes unlikely. (4) Elacqua, E.; Zheng, X.; Shillingford, C.; Liu, M.; Weck, M. The ability to synthesize ordered nanomaterials from highly Molecular Recognition in the Colloidal World. Acc. Chem. Res. 2017, 50 (11), 2756−2766. disperse building blocks solves a persistent problem in colloidal ’ self-assembly, as producing uniform nanoparticles is often (5) O Brien, M. N.; Jones, M. R.; Mirkin, C. A. The Nature and Implications of Uniformity in the Hierarchical Organization of impractical at the relevant quantities required to synthesize − 40 Nanomaterials. Proc. Natl. Acad. Sci. U. S. A. 2016, 113 (42), 11717 bulk solids. Additionally, the facile manipulation of the 11725. various structural features of NCTs allows them to provide (6) Shevchenko, E. V.; Talapin, D. V.; Kotov, N. A.; O’Brien, S.; insight into how particle crystallization occurs when “soft” Murray, C. B. Structural Diversity in Binary Nanoparticle Super- bonds drive the assembly process. Moreover, NCTs are lattices. Nature 2006, 439 (7072), 55−59.

5779 DOI: 10.1021/acs.nanolett.9b02508 Nano Lett. 2019, 19, 5774−5780 Nano Letters Letter

(7) Kotov, N. A.; Meldrum, F. C.; Wu, C.; Fendler, J. H. (26) Matyjaszewski, K.; Xia, J. Atom Transfer Radical Polymer- Monoparticulate Layer and Langmuir-Blodgett-Type Multiparticulate ization. Chem. Rev. 2001, 101 (9), 2921−2990. Layers of Size-Quantized Cadmium Sulfide Clusters: A Colloid- (27) Fukuda, T.; Ma, Y. D.; Inagaki, H. Free-Radical Copolymeriza- Chemical Approach to Superlattice Construction. J. Phys. Chem. 1994, tion. 3. Determination of Rate Constants of Propagation and 98 (11), 2735−2738. Termination for Styrene/Methyl Methacrylate System. A Critical (8) Zheng, N.; Fan, J.; Stucky, G. D. One-Step One-Phase Synthesis Test of Terminal-Model Kinetics. Macromolecules 1985, 18 (1), 17− of Monodisperse Noble-Metallic Nanoparticles and Their Colloidal 26. Crystals. J. Am. Chem. Soc. 2006, 128 (20), 6550−6551. (28) Milner, S. T.; Witten, T. A.; Cates, M. E. Effects of (9) O’Brien, M. N.; Jones, M. R.; Brown, K. A.; Mirkin, C. A. Polydispersity in the End-Grafted Polymer Brush. Macromolecules Universal Noble Metal Nanoparticle Seeds Realized Through Iterative 1989, 22 (2), 853−861. Reductive Growth and Oxidative Dissolution Reactions. J. Am. Chem. (29) Bentz, K. C.; Savin, D. A. Chain Dispersity Effects on Brush Soc. 2014, 136 (21), 7603−7606. Properties of Surface-Grafted Polycaprolactone-Modified Silica Nano- (10) Tao, A.; Sinsermsuksakul, P.; Yang, P. Tunable Plasmonic particles: Unique Scaling Behavior in the Concentrated Polymer Lattices of Silver Nanocrystals. Nat. Nanotechnol. 2007, 2 (7), 435− Brush Regime. Macromolecules 2017, 50 (14), 5565−5573. 440. (30) Dodd, P. M.; Jayaraman, A. Monte Carlo Simulations of (11) Liu, W.; Tagawa, M.; Xin, H. L.; Wang, T.; Emamy, H.; Li, H.; Polydisperse Polymers Grafted on Spherical Surfaces. J. Polym. Sci., Yager, K. G.; Starr, F. W.; Tkachenko, A. V.; Gang, O. Diamond Part B: Polym. Phys. 2012, 50 (10), 694−705. Family of Nanoparticle Superlattices. Science 2016, 351 (6273), 582− (31) Jiang, X.; Zhao, B.; Zhong, G.; Jin, N.; Horton, J. M.; Zhu, L.; 586. Hafner, R. S.; Lodge, T. P. Microphase Separation of High Grafting (12) Lo, P. K.; Karam, P.; Aldaye, F. A.; McLaughlin, C. K.; Density Asymmetric Mixed Homopolymer Brushes on Silica Particles. Hamblin, G. D.; Cosa, G.; Sleiman, H. F. Loading and Selective Macromolecules 2010, 43 (19), 8209−8217. Release of Cargo in DNA Nanotubes with Longitudinal Variation. (32) Phillips, C. L.; Glotzer, S. C. Effect of Nanoparticle Nat. Chem. 2010, 2 (4), 319−328. Polydispersity on the Self-Assembly of Polymer Tethered Nano- (13) McMillan, J. R.; Brodin, J. D.; Millan, J. A.; Lee, B.; Olvera de la spheres. J. Chem. Phys. 2012, 137 (10), 104901. Cruz, M.; Mirkin, C. A. Modulating Nanoparticle Superlattice (33) Choi, J.; Hui, C. M.; Schmitt, M.; Pietrasik, J.; Margel, S.; Structure Using Proteins with Tunable Bond Distributions. J. Am. Matyjazsewski, K.; Bockstaller, M. R. Effect of Polymer-Graft Chem. Soc. 2017, 139 (5), 1754−1757. Modification on the Order Formation in Particle Assembly Structures. − (14) McMillan, R. A.; Paavola, C. D.; Howard, J.; Chan, S. L.; Langmuir 2013, 29 (21), 6452 6459. Zaluzec, N. J.; Trent, J. D. Ordered Nanoparticle Arrays Formed on (34) Bolhuis, P. G.; Kofke, D. A. Monte Carlo Study of Freezing of Engineered Chaperonin Protein Templates. Nat. Mater. 2002, 1 (4), Polydisperse Hard Spheres. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, − 247. Relat. Interdiscip. Top. 1996, 54 (1), 634 643. (15) Medalsy, I.; Dgany, O.; Sowwan, M.; Cohen, H.; Yukashevska, (35) Pusey, P. N. The Effect of Polydispersity on the Crystallization − A.; Wolf, S. G.; Wolf, A.; Koster, A.; Almog, O.; Marton, I.; et al. SP1 of Hard Spherical Colloids. J. Phys. (Paris) 1987, 48 (5), 709 712. Protein-Based Nanostructures and Arrays. Nano Lett. 2008, 8 (2), (36) Park, S. Y.; Lytton-Jean, A. K. R.; Lee, B.; Weigand, S.; Schatz, − G. C.; Mirkin, C. A. DNA-Programmable Nanoparticle Crystalliza- 473 477. − (16) Zhang, J.; Santos, P. J.; Gabrys, P. A.; Lee, S.; Liu, C.; tion. Nature 2008, 451 (7178), 553 556. Macfarlane, R. J. Self-Assembling Nanocomposite Tectons. J. Am. (37) Kalsin, A. M.; Fialkowski, M.; Paszewski, M.; Smoukov, S. K.; Chem. Soc. 2016, 138 (50), 16228−16231. Bishop, K. J. M.; Grzybowski, B. A. Electrostatic Self-Assembly of Binary Nanoparticle Crystals with a Diamond-Like Lattice. Science (17) Lynd, N. A.; Meuler, A. J.; Hillmyer, M. A. Polydispersity and − Block Copolymer Self-Assembly. Prog. Polym. Sci. 2008, 33 (9), 875− 2006, 312 (5772), 420 424. 893. (38) Xia, Y.; Nguyen, T. D.; Yang, M.; Lee, B.; Santos, A.; Podsiadlo, (18)Si,K.J.;Chen,Y.;Shi,Q.;Cheng,W.Nanoparticle P.; Tang, Z.; Glotzer, S. C.; Kotov, N. A. Self-Assembly of Self- Superlattices: The Roles of Soft Ligands. Adv. Sci. 2018, 5 (1), Limiting Monodisperse Supraparticles from Polydisperse Nano- particles. Nat. Nanotechnol. 2011, 6 (9), 580−587. 1700179. ̈ (19) Ye, X.; Zhu, C.; Ercius, P.; Raja, S. N.; He, B.; Jones, M. R.; (39) Thunemann, A. F.; Rolf, S.; Knappe, P.; Weidner, S. In Situ Analysis of a Bimodal Size Distribution of Superparamagnetic Hauwiller, M. R.; Liu, Y.; Xu, T.; Alivisatos, A. P. Structural Diversity − in Binary Superlattices Self-Assembled from Polymer-Grafted Nano- Nanoparticles. Anal. Chem. 2009, 81 (1), 296 301. crystals. Nat. Commun. 2015, 6, 10052. (40) Hatton, B.; Mishchenko, L.; Davis, S.; Sandhage, K. H.; (20) Jishkariani, D.; Elbert, K. C.; Wu, Y.; Lee, J. D.; Hermes, M.; Aizenberg, J. Assembly of Large-Area, Highly Ordered, Crack-Free Inverse Opal Films. Proc. Natl. Acad. Sci. U. S. A. 2010, 107 (23), Wang, D.; van Blaaderen, A.; Murray, C. B. Nanocrystal Core Size and − Shape Substitutional Doping and Underlying Crystalline Order in 10354 10359. Nanocrystal Superlattices. ACS Nano 2019, 13 (5), 5712−5719. (21) Macfarlane, R. J.; Thaner, R. V.; Brown, K. A.; Zhang, J.; Lee, B.; Nguyen, S. T.; Mirkin, C. A. Importance of the DNA “Bond” in Programmable Nanoparticle Crystallization. Proc. Natl. Acad. Sci. U. S. A. 2014, 111 (42), 14995−15000. (22) Humphreys, F. J. A Unified Theory of Recovery, Recrystalliza- tion and Grain Growth, Based on the Stability and Growth of Cellular MicrostructuresI. The Basic Model. Acta Mater. 1997, 45 (10), 4231−4240. (23) Brown, R. A. Theory of Transport Processes in Single Crystal Growth from the Melt. AIChE J. 1988, 34 (6), 881−911. (24) Jin, R.; Wu, G.; Li, Z.; Mirkin, C. A.; Schatz, G. C. What Controls the Melting Properties of DNA-Linked Gold Nanoparticle Assemblies? J. Am. Chem. Soc. 2003, 125 (6), 1643−1654. (25) Auyeung, E.; Li, T. I. N. G.; Senesi, A. J.; Schmucker, A. L.; Pals, B. C.; de la Cruz, M. O.; Mirkin, C. A. DNA-Mediated Nanoparticle Crystallization into Wulff Polyhedra. Nature 2014, 505 (7481), 73−77.

5780 DOI: 10.1021/acs.nanolett.9b02508 Nano Lett. 2019, 19, 5774−5780